Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
  long long a[1001],i,ma=100000,p,n;
  long double m1,m2;
int main(){
  cin>>n;
  for(;i<n;i++)cin>>a[i];
  sort(a,a+n);
  m1=(double)(a[n-1]+a[n-2])/(a[1]-a[0]);
  for(i=n-1;i>0;i--)if(a[i]-a[i-1]<=ma){
    ma=a[i]-a[i-1];
    p=i;
  }
  for(i=n-1;i>0;i-=2)if(i!=p){
    m2=(double)(a[i-1]+a[i])/(a[p]-a[p-1]);
    break;
  }
  m1=max(m1,m2);
  printf("%.9Lf\n",m1);
}